Answer
$x=\left\{ -1,\dfrac{2}{5} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
5x^2+3x-2=0
,$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{5}\cdot(5x^2+3x-2)=(0)\cdot\dfrac{1}{5}
\\\\
x^2+\dfrac{3}{5}x-\dfrac{2}{5}=0
\\\\
x^2+\dfrac{3}{5}x=\dfrac{2}{5}
\\\\
x^2+\dfrac{3}{5}x+\left( \dfrac{3}{5\cdot2}\right)^2=\dfrac{2}{5}+\left( \dfrac{3}{5\cdot2}\right)^2
\\\\
x^2+\dfrac{3}{5}x+\dfrac{9}{100}=\dfrac{2}{5}+\dfrac{9}{100}
\\\\
x^2+\dfrac{3}{5}x+\dfrac{9}{100}=\dfrac{40}{100}+\dfrac{9}{100}
\\\\
\left( x+\dfrac{3}{10}\right)^2=\dfrac{49}{100}
\\\\
x+\dfrac{3}{10}=\pm\sqrt{\dfrac{49}{100}}
\\\\
x+\dfrac{3}{10}=\pm\dfrac{7}{10}
\\\\
x=-\dfrac{3}{10}\pm\dfrac{7}{10}
\\\\
x=-\dfrac{3}{10}-\dfrac{7}{10}
\\\\
x=-\dfrac{10}{10}
\\\\
x=-1
,\\\\\text{OR}\\\\
x=-\dfrac{3}{10}+\dfrac{7}{10}
\\\\
x=\dfrac{4}{10}
\\\\
x=\dfrac{2}{5}
.\end{array}
Hence, $
x=\left\{ -1,\dfrac{2}{5} \right\}
.$
